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2020 AMC 10A Problem 19

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2020 AMC 10A Problem 19AMC 10 Step by Step

Name: Date: September 13, 2026

Basic Counting · difficulty 4 of 5 · about 6 min · position P16-20

As shown in the figure below, a regular dodecahedron (the polyhedron consisting of $12$ congruent regular pentagonal faces) floats in empty space with two horizontal faces. Note that there is a ring of five slanted faces adjacent to the top face, and a ring of five slanted faces adjacent to the bottom face. How many ways are there to move from the top face to the bottom face via a sequence of adjacent faces so that each face is visited at most once and moves are not permitted from the bottom ring to the top ring?

A)
$125$
B)
$250$
C)
$405$
D)
$640$
E)
$810$

2020 AMC 10A Problem 19

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